The development of simple and reliable high stability clock lasers is of great importance for future state-of-the-art optical clocks [1]-[5] and for future transportable optical clocks [6], [7]. Further development of clock lasers with better stability has so far been hindered by thermal noise in the reference cavity used for laser stabilization and conventional approaches for improvements may be technically challenging. It has been proposed [8]-[11] to improve the stability and reduce the complexity of state-of-the-art laser frequency stabilization by exploiting cavity QED systems consisting of atoms with a narrow optical transition coupled to a single mode of an optical cavity. The laser stabilization performance of a cavity QED system is affected by a number of system parameters such as the finite temperature of the atoms, the number of involved atoms and the laser power [12]-[14]. However, the dynamics of those elements have not yet been fully explored. Here we present a simple cavity QED system consisting of laser cooled strontium-88 atoms coupled to an optical cavity. We relate measurable quantities to the complex transmission coefficient which relates the input field to the output field. The optimal input power for stabilizing a laser to this system is experimentally determined and the optimal shot-noise-limited linewidth of the system is evaluated to 500 mHz. Furthermore, theoretical shot-noise-limited linewidths of similar cavity QED systems are evaluated for a number of different two electron systems.
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